Titolo della tesi: Multi-year stochastic modelling for market and underwriting risks in non-life insurance
Nowadays, all EU insurance companies are requested by Solvency II to calculate capital requirements to prevent the risk of insolvency. This can be achieved either in accordance with the Standard Formula or using a full or partial Internal Model. An Internal Model is based on a market-consistent valuation of balance sheet items at a one-year time span, where a real-world probabilistic structure is used for the first projection year. In this thesis, we examine the main risks of a non-life insurer, i.e. the non-life underwriting risk and market risk, and their interactions, focusing on the non-life premium and reserve risk, equity risk, property risk, and interest rate risk. Consequently, we quantify the risk profile either with the Standard Formula or using a partial Internal Model. This analysis is performed using some reference stochastic models in the practical insurance business, i.e. the Collective Risk Model for non-life premium risk, the Re-Reserving Model for non-life reserve risk, the Geometric Brownian Motion for equity and property risk, and a real-world version of the G2++ Model for interest rate risk. In this thesis, we also consider a stochastic model for inflation, explicitly affecting the non-life underwriting items. We extend a real-world version of the Jarrow-Yildirim model, assuming that both the nominal rate and real rate evolve according to a two-factor process. It is indeed quite common that a two-factor model is preferred in order to admit some correlations between different rates. Finally, we illustrate a case study and several analyses on a multi-line insurance company in order to see how the risk drivers behave in both a stand-alone and an aggregate framework, and we calibrate the parameters on current and real market data.